1-20 of 54 Search Results for

differential equations

Follow your search
Access your saved searches in your account

Would you like to receive an alert when new items match your search?
Close Modal
Sort by
Series: ASM Failure Analysis Case Histories
Volume: 3
Publisher: ASM International
Published: 01 December 2019
DOI: 10.31399/asm.fach.v03.c9001851
EISBN: 978-1-62708-241-9
... Ω m Ω t + Ω 2 t Equation 31 is thus a linear system of second-order differential equations, with time-dependent coefficients. Although there are no analytical solutions for such systems of equations, numerical methods of calculation are possible. A method known as spectral...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003526
EISBN: 978-1-62708-180-1
... physical relationships of equilibrium/strain compatibility and material constitutive behavior/boundary conditions be satisfied. Classical theory of elasticity ( Ref 1 , 2 , 3 ) involves developing complex differential equations to satisfy these requirements, but such an approach is practical only...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003516
EISBN: 978-1-62708-180-1
.... This may be accomplished using equations or computational mechanics (finite-element analysis). One needs to know the geometries and the materials as well as the processing history and mechanical properties of the materials. Thus far, this article has briefly discussed the mechanics, the structures...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006773
EISBN: 978-1-62708-295-2
... relationships of equilibrium/strain compatibility and material constitutive behavior/boundary conditions be satisfied. Classical theory of elasticity ( Ref 1 – 3 ) involves developing complex differential equations to satisfy these requirements, but such an approach is practical only for situations where closed...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
..., and a procedure to deal with stress by determining maximum values through stress transformation is described. The article provides the stress analysis equations of typical component geometries and discusses some of the implications of the stress analysis relative to failure in components. It focuses on linear...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
... sign. Contemporary models to predict plastic deformation utilize the “flow” (i.e., yield) surface via the plastic potential equation. Because any linear model to predict flow (e.g., the Tresca criterion) is discontinuous in principal stress space, it cannot predict plastic strains for several loading...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003517
EISBN: 978-1-62708-180-1
... are called “long-term” or “extended” overheating failures. Such a failure results from a relatively continuous extended period of slight overheating (differential between design and actual operating temperatures), a slowly increasing level of temperature or stress, or accumulation from several periods...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.9781627081801
EISBN: 978-1-62708-180-1
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006819
EISBN: 978-1-62708-329-4
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.process.c9001595
EISBN: 978-1-62708-235-8
... through-thickness distance hardness profile. The individual alloying element contributions and complicated regression equations typically used are included in ASTM A 255 and SAE J406. It has been demonstrated that almost all elements have a measurable effect on steel hardenability. Carbon has...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003546
EISBN: 978-1-62708-180-1
... propagating into the substrate material of a thin-walled blade. Courtesy of Ashok Koul, Life Prediction Technologies, Inc. With this knowledge it should be possible to: Define the conditions for which empirical, experimentally based, life-prediction equations may be used Develop an appropriate...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006804
EISBN: 978-1-62708-329-4
... pressure-impulse diagrams, or closed-form energy equations that predict maximum responses of an equivalent single-degree-of-freedom or multi-degree-of-freedom system. Using these methods requires a selection of failure criteria, typically based on either ductility ratio or support rotation. Structures...
Series: ASM Handbook
Volume: 11A
Publisher: ASM International
Published: 30 August 2021
DOI: 10.31399/asm.hb.v11A.a0006823
EISBN: 978-1-62708-329-4
.... Alkire R. and Nicolaides G. , Differential Aeration Corrosion of a Passivating Metal under a Moist Film of Locally Variable Thickness , J. Electrochem. Soc. , Vol 121 ( No. 2 ), Feb 1974 , p 183 , 10.1149/1.2401778 11. Alkire R. and Nicolaides G. , The Existence...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006781
EISBN: 978-1-62708-295-2
... and approximate dimensions of the SSTG casing, including a schematic of the steam passageways where the majority of the service cracks were found during inspection. The SSTG start-up loading diagram is shown in Fig. 11(a) ( Ref 29 ). The transient temperature differentials computed for the initial loading...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003551
EISBN: 978-1-62708-180-1
... properties greatly influenced by temperature. Such an equation has often been used to describe the penetration of liquids in refractories without distinction between physical and chemical invasion. However, in the case of chemical invasion, the penetration-dissolution causes changes in composition (which...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003558
EISBN: 978-1-62708-180-1
... between polymers and metals. Wear also can be classified in relative terms as mild and severe. This classification is based on the nature of the wear, not the amount. The differentiation is primarily in terms of the features of the wear scars and secondarily by wear rate. Coarse features and high wear...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.steel.c9001149
EISBN: 978-1-62708-232-7
... lengths of rolled and welded COR-TEN steel plate butt welded together on site. The pipe sustained local buckling and cracking, then fractured during the first five months of operation. Failure was due to low cycle fatigue and fast fracture caused by differential thermal expansion stresses. Thermal lag...
Series: ASM Failure Analysis Case Histories
Publisher: ASM International
Published: 01 June 2019
DOI: 10.31399/asm.fach.power.c9001396
EISBN: 978-1-62708-229-7
... and corrosion will develop. In addition to being present as a surface film, magnetite in a soft powdery form is frequently found in boiler tubes as a corrosion product of iron and as such is often present in the pits and scabs which arise from normal corrosion, differential aeration corrosion, or deposit attack...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003514
EISBN: 978-1-62708-180-1
... (or reliability) analysis depends on the number of failure equations required to describe the structural behavior. A system reliability analysis is required if a structure is composed of multiple components, has multiple failure modes, and/or has multiple failure locations, for example, multi-site damage. In each...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006779
EISBN: 978-1-62708-295-2
... on the finite-life line, P R ( N R / S a R ), the equation of the finite-life line is: (Eq 5) N = N R · ( S a R / S a ) k where k is the slope of the finite-life line. The slope k is typically characterized by values between 3 and 15. A low slope corresponds...